Define modulation index. Why is its value kept, in practice, less than one?

Modulation index is a measure of the extent of modulation done on a carrier signal. In Amplitude modulation, it is defined as the ratio of the amplitude of the modulating signal to that of the carrier signal. m = Am/Ac

Its value is kept less than 1 to avoid overmodulation, which leads to distortions in the modulated signal and makes it very hard to demodulate and extract the modulating signal.

From the given data, m = Am/Ac = Am/500.5 = Am/50
Am = 25V

AM wave is given by, x(t) = Ac(1 + mcos(ωmt))cos(ωct)

Hence, amplitude is given by:
Ax = Ac(1 + mcos(ωmt)) = 50(1 + 0.5cos(2π × 10⁴t))

Maximum value of AM wave is xmax = 50 × 1.5 = 75V

Frequency of lower sideband, f1 = fc − fm = 1.5 × 10⁶ − 10⁴ = 1.49 MHz

Frequency of upper sideband, f1 = fc + fm = 1.5 × 10⁶ + 10⁴ = 1.51 MHz